• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.87-92
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• 2010

Let R be a 2-torsion free $\sigma$-prime ring with an involution $\sigma$, U a nonzero square closed $\sigma$-Lie ideal, Z(R) the center of Rand d a derivation of R. In this paper, it is proved that d = 0 or $U\;{\subseteq}\;Z(R)$ if one of the following conditions holds: (1) $d(xy)\;-\;xy\;{\in}\;Z(R)$ or $d(xy)\;-\;yx\;{\in}Z(R)$ for all x, $y\;{\in}\;U$. (2) $d(x)\;{\circ}\;d(y)\;=\;0$ or $d(x)\;{\circ}\;d(y)\;=\;x\;{\circ}\;y$ for all x, $y\;{\in}\;U$ and d commutes with $\sigma$.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.9
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• pp.650-656
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• 2004

This paper presents block and timing diagrams of the DWA(data weighted averaging) to optimize a feedback time delay of the sigma-delta modulator. Through the Matlab modeling, the optimized coefficients of the integrators are obtained to design the modulator. And then the fully differential SC integrators, feedback DAC, 9-level quantizer, and DWA are designed by considering the nonideal characteristics of the modulator. The designed second-order multibit modulator is fabricated in a 0.35$\mu\textrm{m}$ CMOS process. The designed modulator achieves 73dB signal-to-noise ratio and 72dB dynamic range at 1.2Vp-p 585kHz input singal and 52.8MHz sampling frequency.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.50 no.10
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• pp.513-519
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• 2001

This paper proposed a random sigma-delta modulator(RSDM), which is constructed by a 1st order sigma-delta modulator(SDM) and a simple structured random binary generator(RBG). The 1st order SDM produces a switching pulse waveform which has the same low-frequency component as the reference input, while the RBG spreads the distribution of the number of sampling per switching cycle, and thus disperses the spectrum spikes in the output. The relationship between the harmonic spectra and the number of sampling per switching cycle is studied through computer simulations, and the frequency spectra of the RSDM are confirmed in an experimental setup.

• Proceedings of the Microbiological Society of Korea Conference
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• 2005.05a
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• pp.152-153
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• 2005

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.4
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• pp.622-628
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• 2002

Numerical analysis has been carried out for two-dimensional steady and unsteady mixed convection in the annulus between co-rotating horizontal cylinders with a heated inner cylinder. The ratio of annulus gap($\sigma$) is taken from 1 to 10 and the order of mixed-convection parameter B(=Gr/(1+Re)$^2$) varies from 10$^4$to $10^0$. The flow patterns over this parameter range are steady multicellular, oscillatory multicellular or steady unicellular. The addition of co-rotating of both cylinders stabilizes the flow in the annulus and weakens the unsteadiness. Even in the large values of rotating parameter such as of $10^0$/($\sigma$=2) and 10$^2$($\sigma$=10), the flow pattern becomes asymptotic to the steady unicellular flow, like as in the rigid-body rotating flow.

• Bulletin of the Korean Chemical Society
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• v.32 no.12
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• pp.4195-4198
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• 2011

Intramolecular ${\pi}-{\pi}$ and ${\sigma}-{\pi}$ interactions are omnipresent for numerous energetic and structural phenomena in nature, and the exact description of these nonbonding interactions plays an important role in the accurate prediction of the three-dimensional structures for numerous interesting molecular systems such as protein folding and polymer shaping. We have selected two prototype molecular systems for benchmarking calculations of intramolecular ${\pi}-{\pi}$ and ${\sigma}-{\pi}$ interactions. Accurately describing conformational energy of such systems requires highly elaborate but very expensive ab initio methods such as coupled cluster singles, doubles, and (triples) (CCSD(T)). Our calculations reveal a double hybrid density functional incorporating dispersion correction (B2PLYP-D) that agrees excellently with the CCSD(T) results, indicating that B2PLYP-D can serve as a practical method of choice.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.827-833
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• 2017

In this paper, we define a set including of all $f_a$ with $a{\in}R$ generalized derivations of R and is denoted by $f_R$. It is proved that (i) the mapping $g:L(R){\rightarrow}f_R$ given by g (a) = f-a for all $a{\in}R$ is a Lie epimorphism with kernel $N_{{\sigma},{\tau}}$ ; (ii) if R is a semiprime ring and ${\sigma}$ is an epimorphism of R, the mapping $h:f_R{\rightarrow}I(R)$ given by $h(f_a)=i_{{\sigma}(-a)}$ is a Lie epimorphism with kernel $l(f_R)$ ; (iii) if $f_R$ is a prime Lie ring and A, B are Lie ideals of R, then $[f_A,f_B]=(0)$ implies that either $f_A=(0)$ or $f_B=(0)$.

• Journal of Korean Society of Steel Construction
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• v.12 no.3 s.46
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• pp.269-279
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• 2000

It is much expected that steel bridges, which have been damaged by increase of vehicle load and corrosion, need repair or strengthening. In this paper, the stress generated by repair welding under loading are analyzed by three dimensional elasto-plastic analyses. The longer and deeper repair weld line bocemes, the larger the magnitude of transient stress becomes. The magnitude of transient stress generated by repair welding under loading $({\sigma}_y/3,\;{\sigma}_a)$ is similar to summation of stresses generated by repair welding and loading. The longer repair weld line ratio(1/b) becomes, the larger the magnitude of transient stress generated by repair welding under loading bocomes. And, the longer repair weld line ratio(1/b) becomes, the larger the magnitude of in-plane displacement generated by repair welding under loading$({\sigma}_y/3,\;{\sigma}_a)$.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.27 no.2
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• pp.123-129
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• 2017

Objectives: The purpose of this study is to enhance the application of analytical method of polar solvents(alcohols) by GCOTC (gas chromatography open tubular column) through the system suitability test(SST) to estimate the whole chromatographic system performance(integral part). Methods: To perform the SST, carried out repeatability(n=6) as analytical method of polar solvents by GCOTC, got the retention time($t_R$), standard deviation(${\sigma}_{n-1}$) of $t_R$, baseline width($w_b=4{\sigma}_{n-1}$) and calculated dead time($t_m$) by $v_m=d^2{\pi}L(f/4)$ and $v_m=t_m$ x flow rate. Results: In this experiment, obtained the basic data, there were $t_m=2$ min, methanol($t_R=3.569$, ${\sigma}_{n-1}=0.01$, $w_b=0.04$), ethanol ($t_R=3.892$, ${\sigma}_{n-1}=0.004$, $w_b=0.016$), isopropanol($t_R=4.209$, ${\sigma}_{n-1}=0.004$, $w_b=0.016$). By using these data, calculated the corrected retention time($t_R{^{\prime}}$), capacity factor(k), separation factor(${\alpha}$), number of theoretical plate(n) and resolution($R_s$) for SST and got the good results. Conclusions: Through the SST, could reconfirm the whole chromatographic performance system(integral part) for analytical method of polar solvents by GCOTC. Therefore, this analytical method expect to be widely applied at the related areas.